New York was named a finalist Tuesday for a federal “Race to the Top” education grant that could bring $500 million to the cash-strapped state.

In all, 18 states and the District of Columbia are finalists. A final decision is expected in September.

The money would be critical for schools and taxpayers at a time state education aid is set to be cut by $1.4 billion, or about 5 percent. Gov. David Paterson called for the reduction to help close a $9.2 billion deficit in the current state budget. Although the Legislature sought to restore $600 million, Paterson vetoed that, saying the state couldn’t afford it.

“New York is back where it belongs in the Race to the Top,” said state Senate leader John Sampson, a Brooklyn Democrat. “Today, we have moved one step closer to improving all of New York’s schools, so all of New York’s children have the world class education they deserve.”

U.S. Education Secretary Arne Duncan made the announcement in a speech at the National Press Club in Washington.

New York was a finalist in the first round of grants under the competitive process, but failed in January to get what was then estimated to be as much $700 million. The state’s application was weaker then because the Democrat-led Legislature couldn’t agree to expand the number of charter schools in the state, something long opposed by the state’s powerful teacher unions.

Paterson had called that an element critical to giving New York its best chance.

Lawmakers agreed in March to expand opportunities for opening more charter schools and other steps, working with the state Board of Regents and state Education Commissioner David Steiner and New York City schools Chancellor Joel Klein. The number of charters available for the innovative schools will increase to 460 over four years from the current 200.

“I commend the Legislature for approving my proposals to lift the state’s charter school cap, to link teacher evaluations to student performance and provide resources to implement a data system that tracks individual student performance,” Paterson said Tuesday. “These were all areas that the U.S. Department of Education identified as weaknesses in our first application, which failed in large part because the Legislature initially refused to pass these vital reforms.”

In May, Duncan said New York’s charter school cap had cost the state 13 points off the rating on its first grant application. The state placed 15th out of 16 states that applied. Duncan said New York had a “great chance” to win a grant in the second round.

“It’s encouraging that the U.S. Education Department recognized that teachers unions and other key stakeholders came together in New York to enhance learning opportunities for all students,” said New York State United Teachers union President Richard Iannuzzi.

The other states in the finals for this round are Arizona, California, Colorado, Florida, Georgia, Hawaii, Illinois, Kentucky, Louisiana, Maryland, Massachusetts, New Jersey, North Carolina, Ohio, Pennsylvania, Rhode Island, and South Carolina.